A221018 -id:A221018 - cp's OEIS frontend

A298684 Numbers i such that Fibonacci(i) is divisible by i, i+1, and i+2.

60, 540, 660, 1200, 1320, 1620, 2160, 3060, 5580, 6120, 6600, 6720, 8100, 9180, 9240, 9600, 9720, 9900, 11160, 12240, 12300, 12600, 13200, 13440, 13680, 15120, 15360, 18300, 18480, 19440, 19800, 21000, 22500, 24480, 24840, 26880, 27360, 28920, 29400, 30240, 30780

Offset: 1

Alex Ratushnyak, Jan 24 2018

nonn

A subsequence of A217738.

Chai Wah Wu, Table of n, a(n) for n = 1..1000

Cf. A000045, A023172, A217738, A221018, A225219.

[n: n in [2..10^5] | IsZero(Fibonacci(n) mod (n)) and IsZero(Fibonacci(n) mod (n+1)) and IsZero(Fibonacci(n) mod (n+2))]; // Vincenzo Librandi, Jan 27 2018

fQ[n_] := Mod[ Fibonacci@ n, {n, n +1, n +2}] == {0, 0, 0}; Select[60 Range@513, fQ] (* Robert G. Wilson v, Jan 26 2018 *)

from _future_ import division
A298684_list, n, a, b = [], 1, 1, 1
while len(A298684_list) < 1000:
    if not (a % (n*(n+1)*(n+2)//(1 if n % 2 else 2))):
        A298684_list.append(n)
    n += 1
    a, b = b, a+b # Chai Wah Wu, Jan 26 2018

A298685 Numbers i such that Fibonacci(i) is divisible by i, i+1, i+2, and i+3.

Original entry on oeis.org

540, 1200, 1620, 3060, 5580, 9180, 9900, 12600, 13440, 13680, 18300, 19440, 19800, 21000, 24480, 36900, 43200, 49680, 50220, 54120, 57240, 61560, 65880, 81180, 83700, 103680, 104160, 154080, 155520, 156060, 156240, 202440, 229320, 252000, 279000, 298200, 302940

Offset: 1

Alex Ratushnyak, Jan 24 2018

nonn

A subsequence of A298684.

Chai Wah Wu, Table of n, a(n) for n = 1..1000

Cf. A000045, A023172, A217738, A221018, A225219, A298684.

Select[Range[10^5], Function[{i, j}, AllTrue[i + Range[0, 3], Divisible[j, #] &]] @@ {#, Fibonacci@ #} &] (* Michael De Vlieger, Jan 28 2018 *)

isone(n, k) = !(fibonacci(n) % (n+k));
isok(n) = isone(n,0) && isone(n,1) && isone(n,2) && isone(n,3); \\ Michel Marcus, Jan 29 2018

A298686 Numbers i such that Fibonacci(i) is divisible by i+k for k=0,1,2,3,4.

Original entry on oeis.org

13440, 19440, 19800, 24480, 49680, 61560, 104160, 229320, 298200, 311040, 329400, 436800, 471240, 600600, 1202040, 1299600, 1468800, 1564920, 1702800, 2031120, 2352240, 2402400, 2499840, 2762760, 2805600, 2937600, 2962080, 3150840, 3262680, 3405600, 3843840

Offset: 1

Alex Ratushnyak, Jan 24 2018

nonn

A subsequence of A298685.

Chai Wah Wu, Table of n, a(n) for n = 1..147

Cf. A000045, A023172, A217738, A221018, A225219, A298684, A298685.

isone(n, k) = !(fibonacci(n) % (n+k));
isok(n) = isone(n,0) && isone(n,1) && isone(n,2) && isone(n,3) && isone(n,4); \\ Michel Marcus, Jan 28 2018

More terms from Alois P. Heinz, Jan 25 2018

A298687 Numbers i such that Fibonacci(i) is divisible by i+k for k=0..5.

Original entry on oeis.org

13440, 19440, 329400, 600600, 2499840, 3150840, 5590200, 7660800, 69069000, 83980800, 96049800, 98385840, 175472640, 179663400, 237484800, 320498640, 330663600, 375396840, 404351640, 406380240, 429660000, 437940000, 505234800, 574585200, 635980800

Offset: 1

Alex Ratushnyak, Jan 24 2018

nonn

A subsequence of A298686.

Chai Wah Wu, Table of n, a(n) for n = 1..57

Cf. A000045, A023172, A217738, A221018, A225219, A298684, A298685, A298686.

p0 = 0
p1 = 1
for i in range(1,1000000):
  if p1 % i == 0 and p1 % (i+1) == 0 and p1 % (i+2) == 0:
     if p1 % (i+3) == 0 and p1 % (i+4) == 0 and p1 % (i+5) == 0:  print(i)
  p0, p1 = p1, p0+p1

a(9)-a(25) from Chai Wah Wu, Jan 27 2018

A299155 Numbers i such that Fibonacci(i) is divisible by i+k for k=0..6.

Original entry on oeis.org

329400, 175472640, 808214400, 1367566200, 1928871000, 3433706640, 16109533440, 16916445000, 17847413640, 19507068000, 23163310800, 24961167000, 32645743200, 37263088800, 39803400000, 44915270400, 50238568800, 66072283200, 81924990840, 85368457440

Offset: 1

Chai Wah Wu, Feb 03 2018

nonn

A subsequence of A298687.

Cf. A000045, A023172, A217738, A221018, A225219, A298684, A298685, A298686, A298687.

fibomod(n,m) = lift(Mod([0,1;1,1],m)^(n+1))[1,1];
isok(n) = prod(k=0,6,fibomod(n,n+k)==0); \\ Silvester Resnik, May 18 2018

a(7)-a(20) from Silvester Resnik, May 18 2018

A298688 a(n) is the least i such that Fibonacci(i) is divisible by i+k for all k=0..n.

Original entry on oeis.org

1, 60, 60, 540, 13440, 13440, 329400, 175472640, 50238568800

Offset: 0

Alex Ratushnyak, Jan 24 2018

a(0)..a(5) are first terms of sequences A023172, A217738, A298684, A298685, A298686, A298687.

			Least i such that Fibonacci(i) is divisible by i and i+1 (cf. A217738) is i=60, therefore a(1)=60.
Least i such that Fibonacci(i) is divisible by i, i+1, ..., i+5 (cf. A298687) is i=13440, therefore a(5)=13440.

Cf. A000045, A023172, A217738, A221018, A225219, A298684, A298685, A298686, A298687.

a(7) from Alois P. Heinz, Jan 25 2018
a(6) inserted by Chai Wah Wu, Jan 26 2018
a(8) from Silvester Resnik, May 18 2018

A300555 Numbers i such that Fibonacci(i) is divisible by i+k for k = 0..7.

Original entry on oeis.org

175472640, 44915270400, 50238568800, 439287521400, 572836904640, 589596638400, 735284012400, 778042465200, 987189789600, 1261551677400, 1297640010240, 1307130728400, 1569978804240, 1979830125000, 2705598768600

Offset: 1

Silvester Resnik, May 19 2018

nonn

Subsequence of A299155.

Cf. A000045, A023172, A217738, A221018, A225219, A298684, A298685, A298686, A298687.

fibomod(n, m) = lift(Mod([0, 1; 1, 1], m)^(n+1))[1, 1];
isok(n) = prod(k=0, 7, fibomod(n, n+k)==0);

A303585 Numbers i such that Fibonacci(i) is divisible by i+k for k = 0..8.

Original entry on oeis.org

50238568800, 5824121940000, 46919196354240, 50564131254000, 80493123110400, 195778384956000, 307148642236800, 799863695270640

Offset: 1

Silvester Resnik, May 25 2018

Subsequence of A300555.

Cf. A000045, A023172, A217738, A221018, A225219, A298684, A298685, A298686, A298687, A298688, A299155.

fibomod(n, m) = lift(Mod([0, 1; 1, 1], m)^(n+1))[1, 1];
isok(n) = prod(k=0, 8, fibomod(n, n+k)==0);

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A298684 Numbers i such that Fibonacci(i) is divisible by i, i+1, and i+2.

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A298685 Numbers i such that Fibonacci(i) is divisible by i, i+1, i+2, and i+3.

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A298686 Numbers i such that Fibonacci(i) is divisible by i+k for k=0,1,2,3,4.

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A298687 Numbers i such that Fibonacci(i) is divisible by i+k for k=0..5.

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A299155 Numbers i such that Fibonacci(i) is divisible by i+k for k=0..6.

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A298688 a(n) is the least i such that Fibonacci(i) is divisible by i+k for all k=0..n.

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A300555 Numbers i such that Fibonacci(i) is divisible by i+k for k = 0..7.

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A303585 Numbers i such that Fibonacci(i) is divisible by i+k for k = 0..8.

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